3) A carton of 10 batteries contains 2 that are defective. A quality control-ins

Question

3) A carton of 10 batteries contains 2 that are defective. A quality control-inspector chooses a random (31 sample of S batteries. Find the probability that the sample contains (a) none of the defective batteries. (b) one of the defective batteries. (5 polns) (e) at most two of the defective batteries The probability disribution, /(), of a discrete random variable X'is given in the table below (3.3 points) 14) f(x) 0.40 0.25 0.35 (a) Find the probability that the value of X is more than 1. (b) Determine the cumulative probability distribution F(x) = P(S x) of (c) Calculate the mean of the given probability distribution f(x). (d) Calculate the standard deviation of the given probability distribution

Explanation / Answer

Dear Student Thank you for using Chegg !! Total Number of Batteries = 10 Number of Defeective batteries = 2 Sample number of batteries chosen = 5 Total Number of ways of selection of 5 batteries out of 10 is = 10C5 Number of ways of selection such that there are no defective batteries in chosen sample = 8C5 = 56 a) Probability of chosing a sample without defective battery is = 8C5 / 10C5 = 0.22222222 b) Number of ways of selection such that there is one defective batteries in chosen sample = 8C4 * 2C1 = 140 Probability of chosing a sample with one defective battery is = 8C4 * 2C1 / 10C5 0.55555556 c) At most two defective batteries Number of ways of selection such that there is tw0 defective batteries in chosen sample = 8C3 * 2C2 = 56 Probability of chosing a sample with one defective battery is = (8C5 + 8C4*2C1 + 8C3 * 2C2) / 10C5 = 1 Solution

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